Here is a question that my professor posted...
"Assume the price elasticity of demand for U.S. Frisbee. frisbees is -0.6. If the company increases the price of each frisbee from $6 to $8, the number of frisbees sold will:"
The answer is: Decrease by 17.1 percent
What I would like to know is how she got to this answer? I have been trying every formula I can think of and nothing is working.
Thanks!
Mike
Your prof used the mid-point method for calculating percentage change.
Price changed by 2 from 6 to 8. Calculate the pct change from the mid-point. i.e., 2/7 = .2857
.2867 * 0.6 = .1714
QED
To calculate the percentage change in quantity demanded, you need to use the formula:
Percentage change in quantity demanded = (Price elasticity of demand) x (Percentage change in price)
In this case, the price elasticity of demand is given as -0.6, which indicates an inelastic demand.
Using the formula, we can calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = (-0.6) x (Percentage change in price)
The percentage change in price is the difference between the new and old price divided by the old price, multiplied by 100:
Percentage change in price = [(New price - Old price) / Old price] x 100
Plugging the values into the formula, we have:
Percentage change in price = [(8 - 6) / 6] x 100 = (2 / 6) x 100 = 33.33%
Now, let's calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = (-0.6) x 33.33% ≈ -19.99%
Rounding to one decimal place, the percentage change in quantity demanded is approximately -20%.
Therefore, the number of frisbees sold will decrease by 20% when the price increases from $6 to $8.
To determine the change in the quantity of frisbees sold when the price increases from $6 to $8, you can use the concept of price elasticity of demand. The price elasticity of demand measures the responsiveness of quantity demanded to a change in price.
In this case, the price elasticity of demand for U.S. frisbees is given as -0.6. The negative sign indicates that the demand is inversely related to the price. A price elasticity of demand less than -1 indicates elastic demand, meaning that a price increase will result in a proportionally larger decrease in quantity demanded.
To calculate the percentage change in quantity demanded, you need to use the following formula:
Percentage change in quantity demanded = Price elasticity of demand x Percentage change in price
Given that the price increases from $6 to $8, the percentage change in price can be calculated as:
Percentage change in price = (New price - Initial price) / Initial price x 100
= ($8 - $6) / $6 x 100
= $2 / $6 x 100
= 33.33%
Substituting the given price elasticity of demand (-0.6) into the formula, we can calculate the percentage change in quantity demanded:
Percentage change in quantity demanded = -0.6 x 33.33%
= -19.99%
Since the price elasticity of demand is negative, indicating an inverse relationship, we take the absolute value of the percentage change, which gives us 19.99%. Thus, the number of frisbees sold will decrease by approximately 19.99% when the price increases from $6 to $8.
Therefore, the answer "Decrease by 17.1 percent" is incorrect. It should be "Decrease by approximately 19.99%".